Joint Optimization of Detection and Tracking in Adaptive Radar Systems - Advances in Heuristic Signal Processing and Applications - page 111

magnetic echo is first converted to an electrical signal and passed through a signal
processing stage which includes signal conditioning 1 [ 57 ] and detection .Thisis
usually followed by a tracking (also called information processing [ 6 ]or data pro-
cessing [ 12 , 57 ]) stage as illustrated in Fig. 6.1 .
With this traditional treatment of viewing the overall radar system as a concate-
nation of two subsystems, the radar research has been conducted along two distinct
paths, namely “detection theory” and “tracking theory” with not much interaction
between them. The tracking literature mostly assumed that the detection (or signal
processing) stage is a prior and isolated process, providing measurements for the
tracking stage. Given a set of such measurements, most of the studies aim to opti-
mize the tracking filter based on either the minimum mean square error (MMSE) or
the maximum a posteriori (MAP) criterion [ 9 ]. Similarly, researchers in radar sig-
nal processing literature usually assumed no incoming information from the down-
stream tracking algorithms. Their common optimization approach in the detection
phase is first to specify a desired (or acceptable) false alarm probability ( P FA )for
the detector and then maximize the probability of detection ( P D ) with this con-
straint [ 65 ]. The value of P FA is usually selected in view of the radar processor's
computational capacity in handling the maximum number of false alarms. Although
this seems a reasonable criterion, it is only a heuristic one. It neither accounts for
the properties of the downstream tracker, nor it cares for an overall performance
objective.
A reasonable and challenging question is whether parameter decisions made for
the detector and tracker subsystems are optimal for the combined performance of the
overall radar system. Intuitively, one can easily see that thresholding in the detection
phase might have significant influence on downstream tracking performance. In one
extreme case where no thresholding is applied, targets are detected perfectly but
together with lots of false alarms. In the other extreme where the threshold is set
very high, false alarms are greatly reduced but together with a high probability of
missing the targets.
Another equally important question is whether these subsystem level parame-
ters have to be statically optimized or should they rather be adaptive in space and
time. One strongly feels that some adaptation is necessary since the motion of the
target changes both the spatial context and the Signal-to-Noise Ratio (SNR). Yet
another important concern in adaptive optimization of these subsystem level param-
eters might be the operating regime (i.e., transient or steady-state) of the tracking
filter. Depending on how far from its steady-state operating region it is, the filter
could, for example, be fed with more or less false alarms and missed detections.
In this chapter, we focus on answers to these exciting questions. In particular,
we consider the interaction between the detector and the tracker subsystems and
focus on how we can optimally select the operating P FA value 2

of the detector in

1 This includes the processing blocks prior to detection such as analog-to-digital (A/D) conversion,
beamforming, pulse compression, clutter filtering, and Doppler processing [ 57 ].
2 This in turn determines the detector operating point (P FA ,P D ) for a given SNR and hence the
detection threshold.